The periodic solution problem of a relative rotation nonlinear system is considered. Firstly, the relative rotation nonlinear dynamic system is established, which contains nonlinear elastic force, commonly damped force and forcing periodic force. Secondly, the result about the nonexistence of periodic solution of the corresponding autonomous system is obtained, and some results about the existence of periodic solutions of the system are obtained by using the continuation theorem of coincidence degree theory. The significance is that we generalize the existing results of the literature. Finally an example is given to illustrate that our results are right.